The role of acceleration and vorticity in relativistic hydrodynamics

George Prokhorov,Valentin Zakharov,Oleg Teryaev,D Melikhov,I Volobuev

doi:10.1051/epjconf/201922203025

Abstract

The role of vorticity and acceleration in relativistic hydrodynamics is investigated. Particular attention is paid to the effects of vorticity, as well as mixed effects, when the medium has both acceleration and vorticity. Quantumfield corrections to the energy density of free Dirac fields are calculated using the Zubarev density operator. The corresponding nonperturbative formulas are proposed and justified in the particular cases of parallel vorticity and acceleration and zero acceleration.

Highlights

Various quantum field effects associated with the rotation and acceleration of a medium are discovered
The calculation of corrections related to acceleration in the energy density made it possible to show the Unruh effect from the point of view of quantum statistical mechanics in an inertial frame [5]
Based on the obtained perturbative results, we substantiate the nonperturbative formula for a rotating fermion gas in general case of massive fermions. We show that this nonperturbative formula can be strictly derived in the approach with the Wigner function [6]

Summary

Introduction

Various quantum field effects associated with the rotation and acceleration of a medium are discovered. We present the results of the calculation of corrections associated simultaneously with acceleration and vorticity In this case we consider only massless fields. It is worth noting that in the particular case aμ = 0, we obtain confirmation of the conclusion of [4] that all the effects of vorticity are reduced to replacing μ → μ ± |ω|/2 This modification turns out to be valid in the general case of massive fermions. We discuss the general situation when acceleration is not parallel to vorticity In this case, the polynomiality of the energy density is not obvious, and it is not obvious what form the corresponding Sommerfeld integrals have.

Energy density of accelerated fermion gas

Massless Fields

Massive Fields

Perturbative corrections in the general case

Nonperturbative formula in the case of parallel a and ω

Conclusions